Abstract
Let us imagine having to design an elastic vertical pillar that must transmit an axial compressive load. We know the extents of the upper and of the lower cross-sections of the pillar and its longitudinal length, but the profile of the lateral surface is arbitrary. We want to find the shape of this lateral surface in order that the distibution of the normal stresses at the bottom is as uniform as possible. A partial answer to the problem is given in two-dimensional elastostatics.
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Villaggio, P. The pillar of best efficiency. J Elasticity 42, 79–89 (1996). https://doi.org/10.1007/BF00041224
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DOI: https://doi.org/10.1007/BF00041224